Not as far as I know.
If you travelled there through a portal, you can’t build a base. You can only do it if you travelled there by ship or teleport. The other bases you see during the weekend quests got there by cheating.
But our method is NOT cheating. It’s using a legitimate game mechanic. Yes, it’s a sneaky workaround… but it’s legal.
I should point out that I am not suggesting people should build bases on the Egg planet. I haven’t, and I hope nobody else from CSD will. It spoils the game for other players.
We are building in the system next door to the Egg system - so we can travel to the Egg planet easily, and see what’s going on, without the restrictions that portal travel imposes. We’re not bothering anyone.
In order to take part in the quest, rather than just observe, it’s likely that we will also have to portal to the Egg planet. That seems to be the way these quests work.